Influence of Rotation on Fingering Convection in Planetary Cores

TL;DR

This work addresses fingering convection in a thick, stably stratified layer atop planetary cores under rotation, focusing on how the ratio $N^2/\Omega^2$ controls flow morphology and transport. The authors employ 3D rotating spherical-shell simulations with double-diffusive buoyancy (temperature and composition) and fixed Lewis number, exploring weak, intermediate, and rapid rotation regimes. They find laminar, narrow fingers that reorient from radial to columnar as $N^2/\Omega^2$ increases, and they uncover rich, rotation-driven large-scale dynamics including zonal flows, axisymmetric/spiraling bands, finger clusters with toroidal gyres, and hemispherical modes, all of which may interact with dynamo fields in Mercury’s core. The results highlight the potential for stable-layer fingering convection to influence magnetic field morphology through differential rotation and localized mixing, while noting the need for magnetic-field feedback studies and simulations at planetary Ekman numbers to assess real-core relevance.

Abstract

Stably stratified layers are thought to develop at the top of the liquid metallic cores of many terrestrial planets. We consider the case where the thermal gradient is stable but the compositional gradient is unstable, a situation particularly relevant to Mercury. The strong contrast between molecular diffusivities of temperature and composition leads to fingering convection. We investigate this process using hydrodynamical simulations in a rotating spherical shell, systematically varying the stratification strength N relative to the rotation rate $Ω$. In all regimes, the primary fingering mode forms narrow, elongated structures that shift orientation from the rotation axis to the direction of gravity as $N^2/Ω^2$ exceeds 10. The fingers remain laminar, with transverse scales proportional to thermal stratification but independent of rotation. Fingering convection also drives secondary large-scale flows across most of the explored parameter space, producing diverse dynamics including zonal flows, hemispherical convection, axisymmetric poloidal bands, finger clusters, and toroidal gyres. In the rapidly-rotating regime, laterally inhomogeneous mixing generates zonal flows in thermo-compositional wind balance; zonal flow direction and amplitude depend on $N^2/Ω^2$, with amplitude weakening for strong stratification $N^2/Ω^2>10$. In the intermediate regime ($N^2/Ω^2\sim 1$), axisymmetric or spiraling poloidal bands emerge within the tangent cylinder, gradually overtaking the primary fingers. For stronger stratification, finger clusters and weak, large-scale density anomalies surrounded by toroidal gyres form in the upper domain. These diverse large-scale flows may interact with the dynamo-generated magnetic field in the deeper core, potentially influencing surface magnetic fields.

Figures (20)

• Figure 1: Simulations in the parameter space $\hbox{Ek}-\hbox{Ra}_c$. All the simulations were performed with $\hbox{Le}=10$, $\hbox{Pr}=0.3$ and $R_{\rho}^i=\hbox{Le}/3$. The lower (upper) dashed line represents $N^2/\Omega^2=1$ ($N^2/\Omega^2=10$ respectively). Series 1 simulations are represented in red and Series 2 simulations in blue. Columnar/radial/bands refer to the structure of the radial flows in the rapidly-rotating/weakly-rotating/intermediate regimes. The location of the finger clusters (§\ref{['sec:cluster']}) is indicated by large open circles.
• Figure 2: Isosurfaces of the radial velocity for two representative cases of (a) $N^2/\Omega^2\gg1$ ($Ek=10^{-1}$ in Series 1) and (b) $N^2/\Omega^2\ll 1$ ($Ek=10^{-4}$ in Series 1). Red (blue) indicates positive (negative) values of $u_r$ and the isosurfaces corresponds to 10% of the maximum values of $u_r$ in a given snapshot.
• Figure 3: Spectra of the poloidal kinetic energy as a function of the spherical harmonics degree $l$ for selected cases in Series 1 and 2 in (a)-(b). The spectra are calculated from a snapshot and averaged in radius excluding the boundary layers. In (c), the degree $l$ is normalised by $\mathcal{L}_{theo}= (|\hbox{Ra}_t|/r_o)^{-1/4}$. $N^2/\Omega^2=0.06$ has the same parameters in both Series.
• Figure 4: Radial profile of the r.m.s. radial velocity for selected simulations in Series 2 ($0.25 \leq N^2/\Omega^2\leq 24.9$) and Series 1 ($N^2/\Omega^2=62240$). The vertical dashed line corresponds to the radius $r_s$ where $R_{\rho}(r=r_s)=\hbox{Le}$.
• Figure 5: Variation of (a) the Reynolds number $\hbox{Re}$ and (b) the local Reynolds number $\hbox{Re}_{\mathcal{L}}$ as a function of $N^2/\Omega^2$. Both Reynolds numbers are based on the mean poloidal velocity. The triangles corresponds to the rescaled Reynolds number where fingering convection occurs only outside the tangent cylinder for $N^2/\Omega^2<0.1$. The case $N^2/\Omega^2=0.2$ of Series 1 is represented by two values (linked by a dotted line) corresponding to two states of the zonal flow (see §\ref{['sec:zonal']}).